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7.27 (1980)

Open

Is it true that the group $SL_n(q)$ contains, for sufficiently large $q$, a diagonal matrix which is not contained in any proper irreducible subgroup of $SL_n(q)$ with the exception of block-monomial ones?

Contributor: V. M. Levchuk

Progress

For $n = 2, 3$ the answer is known to be affirmative (V. M. Levchuk, in: Some problems of the theory of groups and rings, Inst. of Physics SO AN SSSR, Krasnoyarsk, 1973 (Russian)). Similar problems are interesting for other Chevalley groups.

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